Types of Angles

Angles are classified on the basis of three properties: based on their measure, sum, and position. however, Acute, Right, Obtuse, Flat, and Reflex angles are some common types of angles in Geometry.

What is an Angle?

An angle is a region of the plane between two rays with a common region called sides having a common originwhat is an An angle vertex. in other words, it is bounded by these two rays or sides starting from the same point known as the vertex. for example, the sum of the angles of a triangle is equal to 180º in total.

the angles are always formed by intersecting two lines with each other. both lines will also coincide from the same vertex to the rest of the sides or points. these angles also have amplitude in degrees that can be measured with the help of a protector.

Types of Angles – A Comparative Chart

Types of Angles - A Comparative Chart 

Types of Angles According to their Measurement

this type of angle measurement refers to simple angles and is a measurement of the opening between two sides of the angle and is always expressed in degrees (º). the degree (º) measurement is also known as sexagesimal degree º which is the amplitude of the angle resulting from dividing the circumference into 360 equal parts.

1 ^ {\ circ} = 60 '= 3600' '

1 '= 60' '


“The Radian (rad) is used when we measure the central angle of a circle whose arc length coincides with the length of its radius.” What is a Radian

1Rad= 57° 17′44.8″

360°= 2πRad

The classification of the angles according to their measure would be:

Acute angles

if the amplitude of an angle is less than 90º (> 90º) it is known as the acute angle. so, all those angles having amplitude fewer than 90º are acute angles. when somebody tries to separate the two adjacent fingers, an acute angle is formed. another way to elaborate on an acute angle is that the angle having inclination is greater than 0 ° and less than 90 °, not including the latter measure. is known as acute. an ice cream cone is a good example of that.

Acute angle diagram

Right angles

if the angle measures exactly 90º, it is known as a right angle. all those angles that measure exactly 90º are right angles. the angles of the square and rectangle are right and measure exactly 90º. the amplitude of the right angle also measures 90° and starts from the vertex having perpendicular sides.

Right angle diagram

Obtuse angles

all the angles measure more than 90º and less than 180º (> 90º and <180º) are obtuse angles. we can also is defined the angles that measure between 90º and 180º. the opening of the wings of some airplanes and the opening of a fan is a good example of such type of angle. they have an amplitude greater than 90 ° and less than 180 °, not including the aforementioned measurements.

Obtuse angle diagram

Flat or Plan angles

flat or plan angles are measured exactly 180º. they also measure 180º and looks like a straight line. a straight angle is formed by joining two right angles. they also have an amplitude measure of 180 °. This angle has a particular characteristic, and that is that its two lines join from the vertex forming an extension in the form of a straight line. For example, when the hands of the clock show 03:45 minutes. In this case, the small hand marks the number three and the large hand marks the number 9. Another example may be when the clock marks 12:30 with its hands, among others.

Plain angle diagram

Concave angles

They are the angles whose amplitude is greater than 180º and less than 360º (> 180º and> 360º). The concave angle is one whose amplitude measures more than 180 °, but less than 360 °. For example, if you have a round cake cut into parts from its center point, but less than half of it has been eaten. The remainder of the paste forms a concave angle.

Concave angle diagram

Convex angles

They are the angles that measure between 0º and 180º (> 0º and> 180º)

Convex angle diagram

Full angles

A complete angle is one that measures, exactly 360º. It looks like a circumference. It is the one that measures 360 °, in this sense, the line that starts it returns to its point of origin. For example, go around the world and finish in the same starting position.

Full angle diagram

Null angle

Measure 0°. The rays that form the angles coincide.

Null angle diagram

Negative angle

Measures less than 0°. The negative angles rotate in the clockwise direction, ie, in the sense that the clockwise move. A negative angle can be converted into a positive angle by adding 360°.

Negative angle diagram

An angle greater than 360 °

It measures more than one lap. An angle of 390° = 360° +30°, if we represent it, it coincides with an angle of 30°. An angle of 750° = 2.360°+30°, if we represent it, it coincides with an angle of 30°. If we want to pass an angle to the first turn, we divide the angle by 360 °: The quotient is the number of turns it makes, and the rest is the resulting angle that corresponds to the first turn.

Angle greater than 360 ° diagram

Types of angles with respect to their sum

When we have two angles, we can classify them as:

  • Complementary angles: are those whose sum is equal to 90º. For example, the complementary angle of a 30º angle is another of 60º (30º + 60º = 90º).

Complementary angles

  • Supplementary angles: are those whose sum is equal to 180º. For example, the supplementary angle of a 30º angle is another 150º (30º + 150º = 180º).

Supplementary angles

Types of Angles According to their position

This difference takes into account the position of one angle with respect to another (s).

Adjacent angles:

The angles are adjacent when one of the sides is shared and the other sides form a straight line (equal to 180º). they are part of the related angles. These have a common vertex and side, but the other sides are made up of opposite rays. The sum of these angles adds up to 180 ° of amplitude.

Adjacent angles diagram

Opposite angles by the vertex:

They have the same vertex while the sides are extensions of each other. We can get opposite angles to the vertex when we open scissors. they are angles that are opposed from the vertex and whose sides are formed by the rays that are opposite of the sides of each angle.

Opposite angles by the vertex

Consecutive angles:

Consecutive angles are those angles that share aside, regardless of their measure or the sum of the two angles. When consecutive angles are formed on one side of a line they add up to 180º. When the angles are consecutive around a point, they add up to 360º. For example, the rudder of a ship has consecutive angles. are those that have the same vertex and side in common. That is, it is at an angle right next to each other.

Consecutive angle diagram

Angles between parallels and a transverse line

Corresponding angles:

The angles 1 Y 2 are equal.

Corresponding angles diagram

Alternate internal angles:

The angles 2 Y 3 are equal.

Alternate internal angles

Alternate Exterior Angles:

The angles 1 Y 4 are equal.

Alternate Exterior Angles

Angles on the circumference

Central angle:

The central angle has its vertex in the center of the circumference and its sides are two radii. The measure of an arc is that of its corresponding central angle.

Central angle

Inscribed angle:

The inscribed angle has its vertex on the circumference and its sides are secant to it. Measure the half of the arch that it covers.

Inscribed angle

Semi-inscribed angle:

The semi-inscribed angle vertex is on the circumference, one side secant and the other tangent to it. Measure the half of the arch that it covers.

Semi-inscribed angle

Inner angle:

Its vertex is inside the circumference and its sides secant to it. Measure half of the sum of the measurements of the arches that cover its sides and the extensions of its sides.

Inner angle

Outside angle:

Its vertex is a point outside the circumference and the sides of its angles are either secant to it, or one tangent and another secant, or tangent to it. Measure half the difference between the measurements of the arches that span their sides on the circumference.

Outside angle

Angles of a regular polygon

Angles of a regular polygon

The central angle of a regular polygon:

It is the one formed by two consecutive radii.


Yes, n is the number of sides of a polygon:


Central angle = = 360° ÷ n

Central angle of regular pentagon = 360° ÷ 5 = 72°

Interior angle of a regular polygon:

It is formed by two consecutive sides.

Inner angle = 180° – Central angle

Interior angle of regular pentagon = 180° -72° = 108°

The exterior angle of a regular polygon:

It is the one formed by one side and the extension of a consecutive side.

The exterior and interior angles are supplementary, that is, they add 180°.

                                         Outside angle = Center angle

An exterior angle of a regular pentagon = 72°

Sum of two angles

The sum of two angles is another angle whose amplitude is the sum of the amplitudes of the two initial angles.

sum of the angles

Subtraction of Two Angles

The subtraction of two angles is another angle whose amplitude is the difference between the amplitude of the greater angle and that of the smaller angle.

Subtraction of Two Angles

Multiplication of a number by an angle

The multiplication of a number by an angle is another angle whose amplitude is the sum of as many angles equal to the given one as indicated by the number.

Multiplication of a number by an angle

Division of an angle by a number

Dividing an angle by a number is finding another angle such that multiplied by that number gives the original angle.

Division of an angle by a number

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